What are the divisors of 389?

1, 389

There is a total of 2 positive divisors.
The sum of these divisors is 390.
The arithmetic mean is 195.

2 odd divisors

1, 389

How to compute the divisors of 389?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 389 by each of the numbers from 1 to 389 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

389 / 1 = 389 (the remainder is 0, so 1 is a divisor of 389)
389 / 2 = 194.5 (the remainder is 1, so 2 is not a divisor of 389)
389 / 3 = 129.66666666667 (the remainder is 2, so 3 is not a divisor of 389)
...
389 / 388 = 1.0025773195876 (the remainder is 1, so 388 is not a divisor of 389)
389 / 389 = 1 (the remainder is 0, so 389 is a divisor of 389)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 389 (i.e. 19.723082923316). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

389 / 1 = 389 (the remainder is 0, so 1 and 389 are divisors of 389)
389 / 2 = 194.5 (the remainder is 1, so 2 is not a divisor of 389)
389 / 3 = 129.66666666667 (the remainder is 2, so 3 is not a divisor of 389)
...
389 / 18 = 21.611111111111 (the remainder is 11, so 18 is not a divisor of 389)
389 / 19 = 20.473684210526 (the remainder is 9, so 19 is not a divisor of 389)